JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Current Electricity

The series combination of two batteries, both of the same emf 10 V, but different internal resistance of

20Ω

and

5Ω

, is connected to the parallel combination of two resistors 30

Ω

and

R Ω

. The voltage difference across the battery of internal resistance

20Ω

is zero, the value of

R

(in

Ω

) is ____.

Answer: 30

Solution

The two cells are in series, so one current

I

flows through both. The terminal voltage of the

20 Ω

cell is zero, which means

ε - I r_{1} = 0

, i.e.

10 - 20 I = 0

, so

I = 0.5

A. The other cell then presents

ε - I r_{2} = 10 - 0.5 (5) = 7.5

V across the parallel pair, and that current splits between

30 Ω

and

R

0.5 = \frac{7.5}{30} + \frac{7.5}{R} = 0.25 + \frac{7.5}{R}

, so

\frac{7.5}{R} = 0.25

and

R = 30 Ω

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Integer answer